# Nonlinear Dynamic Analysis of Pilotis Structures Supported by Drift-Hardening Concrete Columns

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Outline of the Sample Pilotis Buildings

^{2}, and that of the roof floor was 13.2 kN/m

^{2}following the Japanese standard [23], which gave an axial load ratio of 0.14 to the columns in the pilotis story.

## 3. Method of Nonlinear Dynamic Analysis

_{p}and L are the hinge length and the shear span of the column, respectively. The hinge length was assumed to be equal to the depth of the column section (900 mm), and the shear span was 1900 mm. The stiffness of unloading and reloading paths (K

_{un}) can be obtained from

_{o}is the initial stiffness, ϕ

_{un}and ϕ

_{A}are the curvature at unloading and reloading points and the curvature at point A (see Figure 5), respectively, and γ is the reduction factor of unloading and/or reloading stiffness.

## 4. Analytical Results and Discussions

#### 4.1. Static Analysis

#### 4.2. Dynamic Response Analysis

#### 4.2.1. Analysis Method and Input Ground Motions

^{2}for the NS component. The peak ground acceleration (PGA) and the peak ground velocity (PGV) of the three selected earthquakes are listed in Table 2, along with the values of acceleration response S

_{a}(T

_{1}) and velocity response S

_{v}(T

_{1}), corresponding to the fundamental periods (T

_{1}) of the DHCP and DCP models with a damping ratio h = 0.05. Figure 8 displays the original ground acceleration histories and those scaled by PGV = 50 cm/s, the latter of which approximately corresponds to the safety limit of DE recommended in current Japanese design code. The selected earthquake records were scaled by the peak ground velocity (PGV) ranging from 12.5 cm/s to 100 cm/s with an interval of 12.5 cm/s in order to make sure the response maximum inter-story drift ratio of the pilotis story in the DHCP model was close to/beyond 4%.

#### 4.2.2. Maximum and Residual Inter-Story Drift Ratios

#### 4.2.3. Influence of Dynamic Loading on Residual Drift Ratio

#### 4.2.4. Maximum Inter-Story Shear Force

## 5. Conclusions

- The use of DHC columns to support the upper bearing-wall could ensure pilotis buildings sufficient robustness and significantly enhance their resilience. Even subjected to extremely strong earthquakes scaled up by PGV = 100 cm/s, the residual drift ratio of the DHCP story remained close to zero, implying the high recoverability and re-occupancy of the DHCP buildings;
- Not only the inherent self-centering ability but also the shake-down effect contributed to the reduction in residual drift ratio in the DHCP story. On the other hand, the reduction in drift ratio in the DCP story by the shake-down effect varies with earthquake records and should not be expected for the pilotis buildings supported by conventional DC columns;
- To make the most of the high resilience of the DHCP story, the upper bearing-wall should have a larger lateral resistance than the sum of the DHC columns. In other words, if the upper bearing-wall does not have sufficient ultimate lateral resistance, the DHCP story will no longer be the weak point of a pilotis building; careful structural design of the upper bearing-wall is needed to ensure high recoverability of the whole building;
- Because the hysteresis energy dissipation capacity of the DHC columns was poorer than that of the DC columns, the DHCP story generally exhibited larger lateral deformation (larger maximum inter-story drift response) than the DCP story. When subjected to the JMA Kobe earthquake, which is a pulse-like earthquake, however, the maximum inter-story drift ratio of the DHCP story was smaller than that of the DCP story as PGV became larger than 50 cm/s.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Sectional details of the structural elements: (

**a**) column C1 at the first story; (

**b**) wall W1 and the boundary column C2 at the upper stories.

**Figure 6.**Modeling of the moment-curvature relationships for columns C1 at the first story: (

**a**) DHC column; (

**b**) DC column.

**Figure 7.**Comparison of static cyclic performance of the pilotis story of DHCP and DCP models: (

**a**) the lateral force (V) versus inter-story drift ratio (IDR); (

**b**) the residual drift ratio (IDRres) versus inter-story drift ratio (IDR) relationship.

**Figure 9.**Maximum and residual inter-story drift ratios (El Centro): (

**a**) maximum inter-story drift ratio IDRmax; (

**b**) residual inter-story drift ratio IDRres.

**Figure 10.**Maximum and residual inter-story drift ratios (Taft): (

**a**) maximum inter-story drift ratio IDRmax; (

**b**) residual inter-story drift ratio IDRres.

**Figure 11.**Maximum and residual inter-story drift ratios (JMA Kobe): (

**a**) maximum inter-story drift ratio IDRmax; (

**b**) residual inter-story drift ratio IDRres.

**Figure 12.**Maximum and residual inter-story drift ratios: (

**a**) maximum inter-story drift ratio IDRmax; (

**b**) residual inter-story drift ratio IDRres.

**Figure 13.**Response histories of inter-story drift ratios and inter-story shear force at pilotis story (PGV = 75 cm/s): (

**a**) time histories of inter-story drift ratio IDR; (

**b**) inter-story shear force versus inter-story drift ratio ISF-IDR.

**Figure 14.**The moment-curvature response histories at the left column C1 bottom hinge sections of DCP model considered or ignored the P-Δ effect: (

**a**) time histories of full dynamic response time 0–60 s; (

**b**) extracted from 20 to 40 s, the black arrow lines demonstrate the accumulation of drift ratio of DC model in 1.5 cycles of the response history when P-Δ effect was considered.

**Figure 15.**Residual drift ratio versus maximum drift ratio relationships: (

**a**) DCP model; (

**b**) DHCP model.

**Figure 17.**Maximum inter-story shear forces (MISFs) along the building height for the three selected earthquake records and at four levels of ground motions scaled by PGV = 25 cm/s, 50 cm/s, 75 cm/s, and 100 cm/s: (

**a**) El Centro; (

**b**) Taft; (

**c**) JMA Kobe.

Column Model | M_{A}(kN∙m) | ϕ_{A}(rad/mm) | M_{B}(kN∙m) | ϕ_{B}(rad/mm) | M_{C}(kN∙m) | ϕ_{C}(rad/mm) | α | γ |
---|---|---|---|---|---|---|---|---|

DHC | 1970 | 0.33 × 10^{−5} | 3690 | 1.40 × 10^{−5} | 6410 | 5.60 × 10^{−5} | 0.110 | 0.5 |

DC | 2400 | 2730 | 2720 | −0.002 | 0.4 |

Record | PGA (cm/s ^{2}) | PGV (cm/s) | S_{a} (T_{1}) (cm/s^{2}) | S_{v} (T_{1}) (cm/s) | ||
---|---|---|---|---|---|---|

DHCP | DCP | DHCP | DCP | |||

El Centro ^{1} | 341.7 | 33.5 | 577.3 | 665.0 | 37.8 | 39.9 |

Taft ^{1} | 152.7 | 15.7 | 422.4 | 353.9 | 25.3 | 23.1 |

JMA Kobe ^{2} | 818.0 | 90.7 | 2128.2 | 2406.9 | 139.2 | 144.4 |

^{1}Provided by The Building Center of Japan (BCJ).

^{2}Provided by Japan Meteorological Agency (JMA).

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**MDPI and ACS Style**

Yuan, S.; Takeuchi, T.; Sun, Y.
Nonlinear Dynamic Analysis of Pilotis Structures Supported by Drift-Hardening Concrete Columns. *Materials* **2023**, *16*, 6345.
https://doi.org/10.3390/ma16196345

**AMA Style**

Yuan S, Takeuchi T, Sun Y.
Nonlinear Dynamic Analysis of Pilotis Structures Supported by Drift-Hardening Concrete Columns. *Materials*. 2023; 16(19):6345.
https://doi.org/10.3390/ma16196345

**Chicago/Turabian Style**

Yuan, Shiyu, Takashi Takeuchi, and Yuping Sun.
2023. "Nonlinear Dynamic Analysis of Pilotis Structures Supported by Drift-Hardening Concrete Columns" *Materials* 16, no. 19: 6345.
https://doi.org/10.3390/ma16196345